Problem: Simplify the following expression: $z = \dfrac{k^2 - 10k + 9}{k - 9} $
Explanation: First factor the polynomial in the numerator. $ k^2 - 10k + 9 = (k - 9)(k - 1) $ So we can rewrite the expression as: $z = \dfrac{(k - 9)(k - 1)}{k - 9} $ We can divide the numerator and denominator by $(k - 9)$ on condition that $k \neq 9$ Therefore $z = k - 1; k \neq 9$